The concept of artificial satellites circling the earth was introduced to scientific literature by Sir Isaac Newton in 1686. Things have gotten considerably more complicated since that time, however. The basic concepts of an orbit are described in any orbital mechanics or astrodynamics textbook, such as "Fundamentals of Astrodynamics" by Bate et al. or "Orbital Mechanics" by Chobotov, AIAA Education Series, Publisher. The following definitions of these terms will be first provided here, since they are necessary for proper understanding of the present invention.
The earliest satellites placed into space by man were deployed into very low circular orbits. The resulting visibility footprint of one of these satellites was quite small and a single satellite had the added disadvantage of providing only a few minutes of coverage per day. In fact, it was quite common for an observer on the equator to miss being in contact with such a satellite for several days. Raising the satellite to a higher orbital altitude (e.g., .apprxeq.600 nautical miles) helped extend both the coverage footprint, average viewing elevation, and the time in view, but for some missions frequent or even continuous coverage became a requirement. This led to the deployment of early multiple satellite systems, a typical example being the Navy's Transit navigation satellite system. Satellite systems designers were increasingly asked to provide continuous coverage; first, for latitudinal zones and then, for the entire globe.
One of the first constellation designers to study zonal coverage was David Luders. The Englishman, John Walker, was the first to systematize the design of multiple-ring, multiple satellites per ring, constellations and his work contributed greatly to the optimization of a number of multi-satellite systems (e.g., NAVSTAR GPS). A Russian designer, G. Mozhaev, independently came up with similar arrays using a more theoretical approach based on mathematical set and group theory. Polar constellations often employed the concept of "street-of-coverage", and further coverage improvements were made by Beste, Ballard and Rider. More recently, Hanson and Linden have investigated large arrays of low earth orbit "LEO" satellites (40-200 satellites). All of these designers employed circular orbits; and even with this simplification, constellation design was considered at best a difficult and time consuming trial and error exercise.
The motion of any artificial satellite may be described using a number of parameters. The eccentricity, e, is a measure of the amount of ellipticity. An orbit which has a greater eccentricity number is more elliptical. Eccentricity e=0 would describe a circle, any number between 0 and 1 is an ellipse, and the eccentricity number of 1 or greater would be a parabola or a hyperbola, respectively (curves which never close).
For an elliptical orbit, the earth, or the object being orbited, is at one of the focal points of the ellipse. Therefore, the satellite is sometimes closer to the earth than at other times. The apogee is defined as the point of highest altitude of a satellite, while perigee is the point of lowest altitude.
A retrograde orbit is one in which the direction of revolution is opposite to that of the earth. A posigrade or prograde orbit is an orbit in which the satellite revolves around the earth in the same direction as the earth.
The inclination angle i is an angle measured between the plane of the orbit, and a plane of the reference, usually the Equator. An inclination angle i less than 90.degree. is a prograde orbit, while an inclination angle greater than 90.degree. is a retrograde orbit. A 90.degree. orbit is a polar orbit.
The period, T, is a measure of how long the satellite takes to make one entire orbit. Mean anomaly M is another way to describe the position in the orbit. Mean anomaly is a fictitious angle indicating the fraction of 360 degrees corresponding to the fraction of the period through which the satellite has passed at any point of its orbit.
The Right Ascension of the Ascending Node ("RAAN") is an angle between the first point of Aries (.gamma.), a non-rotating celestial reference, and the line of nodes, which is the line forming the intersection of a plane of the orbit and the plane of the equator. The line of nodes gives a measure of the position or orientation of the orbit. The longitude of the ascending node .OMEGA. is the angle between the i unit vector (pointing towards the Greenwich meridian) and the ascending node in the rotating reference.
The argument of perigee .omega. is an angle measured in the plane of the orbit between the point of the ascending node and the nearest point of perigee.
Most practical satellites prior to the invention by the present inventors used relatively simple systems based on circular orbits. The earth was covered symmetrically by multiple satellites, which each operate to cover a section of the earth.
Elliptical orbits have been typically avoided in the art, because of their asymmetries, and the consequent problems that they might cause. However, some individual elliptical orbits and elliptical orbit constellations have been proposed. The Russian Molniya orbit is a posigrade orbit designed for polar and high latitude coverage. Other posigrade orbits have been described by John Draim in his U.S. Pat. Nos. 4,809,935 and 4,854,527.
U.S. Pat. No. 4,809,935 describes a three-satellite constellation giving continuous coverage of the entire Northern hemisphere, and an extension of this constellation to include an equatorial orbit resulting in a four-satellite array giving continuous global coverage of both hemispheres. This latter four satellite array provided somewhat higher elevation coverage in the Northern hemisphere than in the Southern Hemisphere.
U.S. Pat. No. 4,854,527 describes a common period four-satellite array giving continuous global coverage with satellites at a lower altitude range than in the first patent. A discussion of obtaining extra Northern Hemisphere coverage through use of elliptic satellite constellations may be found in ANSER Space Systems Division Note SpSDN 84-1, "Satellite Constellation Design Techniques for Future Space Systems" dated September 1984, by John Draim, and James Cooper. Another application of posigrade elliptic orbits is the ACE and ACE-Prime orbits developed by Mr. A. Turner of Loral Corporation.
The present invention also simplifies the design of the solar panels by requiring no more than 1 or 2 degrees of freedom. In the example orbit discussed herein which is 116.degree. retrograde, the panels need only one degree of freedom. In a similar way, a satellite usually needs to radiate its heat toward cold, empty space. In the present invention, it is much easier to face the satellite in a way that always faces the heat radiators away from the sun.
It is also well known that the earth is not totally spherical, but actually it is rather oblate. That is, the earth is bigger at the bottom than it is at the top. The J.sub.2 harmonic, due to the earth's oblateness, causes the node .OMEGA. and argument of perigee .omega. of an orbit to change. The gravitational pull of the earth's equatorial bulge causes, for example, the orbital plane of an eastbound satellite to swing westward. More generally, the force component is directed towards the Equator. This resultant acceleration causes any satellite to reach the Equator (node) short of the crossing point where it would have reached it on a spherical earth. For each revolution, therefore, the orbit regresses .DELTA. amount. These effects have been the subjects of various attempts at compensation.
Sun synchronous circular orbits are also known. These are orbits where the rotation rate of the right ascension of the ascending node is equal to and in the same direction as, the right ascension rate of the mean sun.